Newmark’s method (Newmark, 1965), employing a sliding block model, is widely used for hazard assessment of landslides and slope failures during devastating earthquakes. In this method, the downward displacement of a rigid block under a given seismic motion is calculated to evaluate overall slope stability based on the resulting displacement magnitude. Typically, seismic motion is applied only along the in two directions (horizontal and vertical Axes in the direction of the slope). In contrast, this study attempts a simple extension of the model to account for all three orthogonal components by including the horizontal axis perpendicular to the slope. In this case, the specific conditions under which the block begins to move differ significantly from those under traditional two-dimensional seismic motion. Furthermore, to keep the model simple, this study treats the block’s motion as one-dimensional along the x-direction rather than calculating full three-dimensional rigid body motion. Therefore, this presented model is referred to as a pseudo-three-dimensional (p3D) model.

A comparative analysis was conducted using this p3D model between a case with seismic motion applied only in the two axes and a case applied in all three axes. The input waveform was recorded at the K-NET HKD127 site during the 2018 Hokkaido Eastern Iburi Earthquake. We varied the slope orientation and calculated the final displacements. The comparison of these residual displacements revealed that the results from the two models are clearly different, strongly suggesting the practical effectiveness and necessity of the proposed p3D model.